LMFDB - Embedded newform 162.8.c.b.55.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [162,8,Mod(55,162)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("162.55"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(162, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	162.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,-8,0,-64,-120] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$50.6063741284$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	162.55
Dual form			162.8.c.b.109.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.00000 + 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-60.0000 - 103.923i) q^{5} +(-188.500 + 326.492i) q^{7} +512.000 q^{8} +960.000 q^{10} +(-300.000 + 519.615i) q^{11} +(-2684.50 - 4649.69i) q^{13} +(-1508.00 - 2611.93i) q^{14} +(-2048.00 + 3547.24i) q^{16} +12168.0 q^{17} +16211.0 q^{19} +(-3840.00 + 6651.08i) q^{20} +(-2400.00 - 4156.92i) q^{22} +(-53196.0 - 92138.2i) q^{23} +(31862.5 - 55187.5i) q^{25} +42952.0 q^{26} +24128.0 q^{28} +(-88608.0 + 153474. i) q^{29} +(134030. + 232147. i) q^{31} +(-16384.0 - 28377.9i) q^{32} +(-48672.0 + 84302.4i) q^{34} +45240.0 q^{35} +114959. q^{37} +(-64844.0 + 112313. i) q^{38} +(-30720.0 - 53208.6i) q^{40} +(56064.0 + 97105.7i) q^{41} +(57524.0 - 99634.5i) q^{43} +38400.0 q^{44} +851136. q^{46} +(-280668. + 486131. i) q^{47} +(340707. + 590122. i) q^{49} +(254900. + 441500. i) q^{50} +(-171808. + 297580. i) q^{52} -1.78776e6 q^{53} +72000.0 q^{55} +(-96512.0 + 167164. i) q^{56} +(-708864. - 1.22779e6i) q^{58} +(893172. + 1.54702e6i) q^{59} +(653419. - 1.13175e6i) q^{61} -2.14448e6 q^{62} +262144. q^{64} +(-322140. + 557963. i) q^{65} +(1.00691e6 + 1.74402e6i) q^{67} +(-389376. - 674419. i) q^{68} +(-180960. + 313432. i) q^{70} -4.06094e6 q^{71} -3.85064e6 q^{73} +(-459836. + 796459. i) q^{74} +(-518752. - 898505. i) q^{76} +(-113100. - 195895. i) q^{77} +(-518616. + 898268. i) q^{79} +491520. q^{80} -897024. q^{82} +(-4.60178e6 + 7.97052e6i) q^{83} +(-730080. - 1.26454e6i) q^{85} +(460192. + 797076. i) q^{86} +(-153600. + 266043. i) q^{88} -1.28930e6 q^{89} +2.02411e6 q^{91} +(-3.40454e6 + 5.89684e6i) q^{92} +(-2.24534e6 - 3.88905e6i) q^{94} +(-972660. - 1.68470e6i) q^{95} +(-4.27794e6 + 7.40961e6i) q^{97} -5.45131e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{2} - 64 q^{4} - 120 q^{5} - 377 q^{7} + 1024 q^{8} + 1920 q^{10} - 600 q^{11} - 5369 q^{13} - 3016 q^{14} - 4096 q^{16} + 24336 q^{17} + 32422 q^{19} - 7680 q^{20} - 4800 q^{22} - 106392 q^{23}+ \cdots - 10902624 q^{98}+O(q^{100}) $ 2 * q - 8 * q^2 - 64 * q^4 - 120 * q^5 - 377 * q^7 + 1024 * q^8 + 1920 * q^10 - 600 * q^11 - 5369 * q^13 - 3016 * q^14 - 4096 * q^16 + 24336 * q^17 + 32422 * q^19 - 7680 * q^20 - 4800 * q^22 - 106392 * q^23 + 63725 * q^25 + 85904 * q^26 + 48256 * q^28 - 177216 * q^29 + 268060 * q^31 - 32768 * q^32 - 97344 * q^34 + 90480 * q^35 + 229918 * q^37 - 129688 * q^38 - 61440 * q^40 + 112128 * q^41 + 115048 * q^43 + 76800 * q^44 + 1702272 * q^46 - 561336 * q^47 + 681414 * q^49 + 509800 * q^50 - 343616 * q^52 - 3575520 * q^53 + 144000 * q^55 - 193024 * q^56 - 1417728 * q^58 + 1786344 * q^59 + 1306837 * q^61 - 4288960 * q^62 + 524288 * q^64 - 644280 * q^65 + 2013817 * q^67 - 778752 * q^68 - 361920 * q^70 - 8121888 * q^71 - 7701278 * q^73 - 919672 * q^74 - 1037504 * q^76 - 226200 * q^77 - 1037231 * q^79 + 983040 * q^80 - 1794048 * q^82 - 9203568 * q^83 - 1460160 * q^85 + 920384 * q^86 - 307200 * q^88 - 2578608 * q^89 + 4048226 * q^91 - 6809088 * q^92 - 4490688 * q^94 - 1945320 * q^95 - 8555885 * q^97 - 10902624 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−4.00000	+	6.92820i	−0.353553	+	0.612372i
$2$	−4.00000	+	6.92820i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	−60.0000	−	103.923i	−0.214663	−	0.371806i	0.738506	−	0.674247i	$-0.235532\pi$
$5$	−60.0000	−	103.923i	−0.214663	−	0.371806i	−0.953168	+	0.302441i	$0.902198\pi$
$6$		0			0
$7$	−188.500	+	326.492i	−0.207715	+	0.359773i	−0.950994	−	0.309208i	$-0.899936\pi$
$7$	−188.500	+	326.492i	−0.207715	+	0.359773i	0.743279	+	0.668981i	$0.233269\pi$
$8$	512.000			0.353553
$9$		0			0
$10$	960.000			0.303579
$11$	−300.000	+	519.615i	−0.0679590	+	0.117708i	−0.898003	−	0.439990i	$-0.854982\pi$
$11$	−300.000	+	519.615i	−0.0679590	+	0.117708i	0.830044	+	0.557698i	$0.188315\pi$
$12$		0			0
$13$	−2684.50	−	4649.69i	−0.338892	−	0.586979i	0.645332	−	0.763902i	$-0.276719\pi$
$13$	−2684.50	−	4649.69i	−0.338892	−	0.586979i	−0.984225	+	0.176923i	$0.943386\pi$
$14$	−1508.00	−	2611.93i	−0.146877	−	0.254398i
$15$		0			0
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	12168.0			0.600687			0.300343	−	0.953831i	$-0.402899\pi$
$17$	12168.0			0.600687			0.300343	+	0.953831i	$0.402899\pi$
$18$		0			0
$19$	16211.0			0.542216			0.271108	−	0.962549i	$-0.412610\pi$
$19$	16211.0			0.542216			0.271108	+	0.962549i	$0.412610\pi$
$20$	−3840.00	+	6651.08i	−0.107331	+	0.185903i
$21$		0			0
$22$	−2400.00	−	4156.92i	−0.0480543	−	0.0832324i
$23$	−53196.0	−	92138.2i	−0.911657	−	1.57904i	−0.811723	−	0.584042i	$-0.801470\pi$
$23$	−53196.0	−	92138.2i	−0.911657	−	1.57904i	−0.0999341	−	0.994994i	$-0.531863\pi$
$24$		0			0
$25$	31862.5	−	55187.5i	0.407840	−	0.706400i
$26$	42952.0			0.479266
$27$		0			0
$28$	24128.0			0.207715
$29$	−88608.0	+	153474.i	−0.674652	+	1.16853i	0.301918	+	0.953334i	$0.402373\pi$
$29$	−88608.0	+	153474.i	−0.674652	+	1.16853i	−0.976570	+	0.215198i	$0.930960\pi$
$30$		0			0
$31$	134030.	+	232147.i	0.808046	+	1.39958i	0.914215	+	0.405229i	$0.132808\pi$
$31$	134030.	+	232147.i	0.808046	+	1.39958i	−0.106169	+	0.994348i	$0.533859\pi$
$32$	−16384.0	−	28377.9i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−48672.0	+	84302.4i	−0.212375	+	0.367844i
$35$	45240.0			0.178355
$36$		0			0
$37$	114959.			0.373110			0.186555	−	0.982445i	$-0.440268\pi$
$37$	114959.			0.373110			0.186555	+	0.982445i	$0.440268\pi$
$38$	−64844.0	+	112313.i	−0.191702	+	0.332038i
$39$		0			0
$40$	−30720.0	−	53208.6i	−0.0758947	−	0.131453i
$41$	56064.0	+	97105.7i	0.127040	+	0.220040i	0.922529	−	0.385929i	$-0.126119\pi$
$41$	56064.0	+	97105.7i	0.127040	+	0.220040i	−0.795488	+	0.605969i	$0.792786\pi$
$42$		0			0
$43$	57524.0	−	99634.5i	0.110334	−	0.191104i	−0.805571	−	0.592499i	$-0.798141\pi$
$43$	57524.0	−	99634.5i	0.110334	−	0.191104i	0.915905	+	0.401395i	$0.131475\pi$
$44$	38400.0			0.0679590
$45$		0			0
$46$	851136.			1.28928
$47$	−280668.	+	486131.i	−0.394321	+	0.682985i	−0.993014	−	0.117994i	$-0.962354\pi$
$47$	−280668.	+	486131.i	−0.394321	+	0.682985i	0.598693	+	0.800979i	$0.295687\pi$
$48$		0			0
$49$	340707.	+	590122.i	0.413709	+	0.716565i
$50$	254900.	+	441500.i	0.288386	+	0.499500i
$51$		0			0
$52$	−171808.	+	297580.i	−0.169446	+	0.293489i
$53$	−1.78776e6			−1.64947			−0.824734	−	0.565521i	$-0.808675\pi$
$53$	−1.78776e6			−1.64947			−0.824734	+	0.565521i	$0.808675\pi$
$54$		0			0
$55$	72000.0			0.0583530
$56$	−96512.0	+	167164.i	−0.0734384	+	0.127199i
$57$		0			0
$58$	−708864.	−	1.22779e6i	−0.477051	−	0.826277i
$59$	893172.	+	1.54702e6i	0.566178	+	0.980649i	0.996939	+	0.0781831i	$0.0249119\pi$
$59$	893172.	+	1.54702e6i	0.566178	+	0.980649i	−0.430761	+	0.902466i	$0.641755\pi$
$60$		0			0
$61$	653419.	−	1.13175e6i	0.368584	−	0.638407i	−0.620760	−	0.784001i	$-0.713176\pi$
$61$	653419.	−	1.13175e6i	0.368584	−	0.638407i	0.989344	+	0.145594i	$0.0465092\pi$
$62$	−2.14448e6			−1.14275
$63$		0			0
$64$	262144.			0.125000
$65$	−322140.	+	557963.i	−0.145495	+	0.252005i
$66$		0			0
$67$	1.00691e6	+	1.74402e6i	0.409005	+	0.708417i	0.994778	−	0.102058i	$-0.0325427\pi$
$67$	1.00691e6	+	1.74402e6i	0.409005	+	0.708417i	−0.585774	+	0.810475i	$0.699209\pi$
$68$	−389376.	−	674419.i	−0.150172	−	0.260105i
$69$		0			0
$70$	−180960.	+	313432.i	−0.0630579	+	0.109219i
$71$	−4.06094e6			−1.34655			−0.673275	−	0.739392i	$-0.735113\pi$
$71$	−4.06094e6			−1.34655			−0.673275	+	0.739392i	$0.735113\pi$
$72$		0			0
$73$	−3.85064e6			−1.15852			−0.579259	−	0.815144i	$-0.696658\pi$
$73$	−3.85064e6			−1.15852			−0.579259	+	0.815144i	$0.696658\pi$
$74$	−459836.	+	796459.i	−0.131914	+	0.228482i
$75$		0			0
$76$	−518752.	−	898505.i	−0.135554	−	0.234786i
$77$	−113100.	−	195895.i	−0.0282322	−	0.0488996i
$78$		0			0
$79$	−518616.	+	898268.i	−0.118345	+	0.204980i	−0.919112	−	0.393996i	$-0.871092\pi$
$79$	−518616.	+	898268.i	−0.118345	+	0.204980i	0.800767	+	0.598976i	$0.204426\pi$
$80$	491520.			0.107331
$81$		0			0
$82$	−897024.			−0.179662
$83$	−4.60178e6	+	7.97052e6i	−0.883391	+	1.53008i	−0.0358439	+	0.999357i	$0.511412\pi$
$83$	−4.60178e6	+	7.97052e6i	−0.883391	+	1.53008i	−0.847547	+	0.530720i	$0.821921\pi$
$84$		0			0
$85$	−730080.	−	1.26454e6i	−0.128945	−	0.223339i
$86$	460192.	+	797076.i	0.0780179	+	0.135131i
$87$		0			0
$88$	−153600.	+	266043.i	−0.0240271	+	0.0416162i
$89$	−1.28930e6			−0.193861			−0.0969305	−	0.995291i	$-0.530902\pi$
$89$	−1.28930e6			−0.193861			−0.0969305	+	0.995291i	$0.530902\pi$
$90$		0			0
$91$	2.02411e6			0.281572
$92$	−3.40454e6	+	5.89684e6i	−0.455829	+	0.789518i
$93$		0			0
$94$	−2.24534e6	−	3.88905e6i	−0.278827	−	0.482943i
$95$	−972660.	−	1.68470e6i	−0.116393	−	0.201599i
$96$		0			0
$97$	−4.27794e6	+	7.40961e6i	−0.475920	+	0.824317i	−0.999619	−	0.0275856i	$-0.991218\pi$
$97$	−4.27794e6	+	7.40961e6i	−0.475920	+	0.824317i	0.523700	+	0.851903i	$0.324551\pi$
$98$	−5.45131e6			−0.585073
$99$		0			0
$100$	−4.07840e6			−0.407840
$101$	−9.95030e6	+	1.72344e7i	−0.960974	+	1.66446i	−0.240910	+	0.970547i	$0.577446\pi$
$101$	−9.95030e6	+	1.72344e7i	−0.960974	+	1.66446i	−0.720064	+	0.693908i	$0.755887\pi$
$102$		0			0
$103$	−3.49992e6	−	6.06204e6i	−0.315594	−	0.546624i	0.663970	−	0.747759i	$-0.268870\pi$
$103$	−3.49992e6	−	6.06204e6i	−0.315594	−	0.546624i	−0.979563	+	0.201135i	$0.935537\pi$
$104$	−1.37446e6	−	2.38064e6i	−0.119817	−	0.207528i
$105$		0			0
$106$	7.15104e6	−	1.23860e7i	0.583175	−	1.01009i
$107$	−4.48063e6			−0.353587			−0.176793	−	0.984248i	$-0.556572\pi$
$107$	−4.48063e6			−0.353587			−0.176793	+	0.984248i	$0.556572\pi$
$108$		0			0
$109$	−1.47074e6			−0.108779			−0.0543893	−	0.998520i	$-0.517321\pi$
$109$	−1.47074e6			−0.108779			−0.0543893	+	0.998520i	$0.517321\pi$
$110$	−288000.	+	498831.i	−0.0206309	+	0.0357338i
$111$		0			0
$112$	−772096.	−	1.33731e6i	−0.0519288	−	0.0899433i
$113$	−1.73893e6	−	3.01192e6i	−0.113373	−	0.196367i	0.803755	−	0.594960i	$-0.202832\pi$
$113$	−1.73893e6	−	3.01192e6i	−0.113373	−	0.196367i	−0.917128	+	0.398593i	$0.869499\pi$
$114$		0			0
$115$	−6.38352e6	+	1.10566e7i	−0.391397	+	0.677920i
$116$	1.13418e7			0.674652
$117$		0			0
$118$	−1.42908e7			−0.800697
$119$	−2.29367e6	+	3.97275e6i	−0.124772	+	0.216111i
$120$		0			0
$121$	9.56359e6	+	1.65646e7i	0.490763	+	0.850027i
$122$	5.22735e6	+	9.05403e6i	0.260629	+	0.451422i
$123$		0			0
$124$	8.57792e6	−	1.48574e7i	0.404023	−	0.699788i
$125$	−1.70220e7			−0.779517
$126$		0			0
$127$	2.10378e7			0.911353			0.455677	−	0.890145i	$-0.349397\pi$
$127$	2.10378e7			0.911353			0.455677	+	0.890145i	$0.349397\pi$
$128$	−1.04858e6	+	1.81619e6i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−2.57712e6	−	4.46370e6i	−0.102880	−	0.178194i
$131$	1.03453e7	+	1.79186e7i	0.402062	+	0.696392i	0.993975	−	0.109610i	$-0.0349602\pi$
$131$	1.03453e7	+	1.79186e7i	0.402062	+	0.696392i	−0.591912	+	0.806002i	$0.701627\pi$
$132$		0			0
$133$	−3.05577e6	+	5.29275e6i	−0.112626	+	0.195075i
$134$	−1.61105e7			−0.578420
$135$		0			0
$136$	6.23002e6			0.212375
$137$	2.65761e7	−	4.60311e7i	0.883016	−	1.52943i	0.0350447	−	0.999386i	$-0.488843\pi$
$137$	2.65761e7	−	4.60311e7i	0.883016	−	1.52943i	0.847971	−	0.530043i	$-0.177824\pi$
$138$		0			0
$139$	9.75045e6	+	1.68883e7i	0.307945	+	0.533376i	0.977913	−	0.209014i	$-0.0670254\pi$
$139$	9.75045e6	+	1.68883e7i	0.307945	+	0.533376i	−0.669968	+	0.742390i	$0.733692\pi$
$140$	−1.44768e6	−	2.50746e6i	−0.0445887	−	0.0772298i
$141$		0			0
$142$	1.62438e7	−	2.81350e7i	0.476078	−	0.824591i
$143$	3.22140e6			0.0921231
$144$		0			0
$145$	2.12659e7			0.579290
$146$	1.54026e7	−	2.66780e7i	0.409598	−	0.709445i
$147$		0			0
$148$	−3.67869e6	−	6.37167e6i	−0.0932775	−	0.161561i
$149$	−4.25782e6	−	7.37475e6i	−0.105447	−	0.182640i	0.808474	−	0.588532i	$-0.200294\pi$
$149$	−4.25782e6	−	7.37475e6i	−0.105447	−	0.182640i	−0.913921	+	0.405893i	$0.866961\pi$
$150$		0			0
$151$	−3.18510e7	+	5.51675e7i	−0.752841	+	1.30396i	0.193599	+	0.981081i	$0.437984\pi$
$151$	−3.18510e7	+	5.51675e7i	−0.752841	+	1.30396i	−0.946440	+	0.322879i	$0.895349\pi$
$152$	8.30003e6			0.191702
$153$		0			0
$154$	1.80960e6			0.0399264
$155$	1.60836e7	−	2.78576e7i	0.346914	−	0.600873i
$156$		0			0
$157$	3.18171e7	+	5.51089e7i	0.656163	+	1.13651i	0.981601	+	0.190945i	$0.0611552\pi$
$157$	3.18171e7	+	5.51089e7i	0.656163	+	1.13651i	−0.325437	+	0.945564i	$0.605512\pi$
$158$	−4.14892e6	−	7.18615e6i	−0.0836827	−	0.144943i
$159$		0			0
$160$	−1.96608e6	+	3.40535e6i	−0.0379473	+	0.0657267i
$161$	4.01098e7			0.757460
$162$		0			0
$163$	6.87301e7			1.24305			0.621527	−	0.783392i	$-0.286512\pi$
$163$	6.87301e7			1.24305			0.621527	+	0.783392i	$0.286512\pi$
$164$	3.58810e6	−	6.21476e6i	0.0635200	−	0.110020i
$165$		0			0
$166$	−3.68143e7	−	6.37642e7i	−0.624652	−	1.08193i
$167$	−6.47171e6	−	1.12093e7i	−0.107525	−	0.186240i	0.807242	−	0.590221i	$-0.200959\pi$
$167$	−6.47171e6	−	1.12093e7i	−0.107525	−	0.186240i	−0.914767	+	0.403981i	$0.867626\pi$
$168$		0			0
$169$	1.69612e7	−	2.93776e7i	0.270304	−	0.468180i
$170$	1.16813e7			0.182356
$171$		0			0
$172$	−7.36307e6			−0.110334
$173$	2.11062e7	−	3.65570e7i	0.309919	−	0.536795i	−0.668425	−	0.743779i	$-0.733031\pi$
$173$	2.11062e7	−	3.65570e7i	0.309919	−	0.536795i	0.978344	+	0.206984i	$0.0663647\pi$
$174$		0			0
$175$	1.20122e7	+	2.08057e7i	0.169429	+	0.293460i
$176$	−1.22880e6	−	2.12834e6i	−0.0169897	−	0.0294271i
$177$		0			0
$178$	5.15722e6	−	8.93256e6i	0.0685402	−	0.118715i
$179$	1.13640e8			1.48096			0.740482	−	0.672076i	$-0.234597\pi$
$179$	1.13640e8			1.48096			0.740482	+	0.672076i	$0.234597\pi$
$180$		0			0
$181$	−1.27922e8			−1.60350			−0.801752	−	0.597658i	$-0.796098\pi$
$181$	−1.27922e8			−1.60350			−0.801752	+	0.597658i	$0.796098\pi$
$182$	−8.09645e6	+	1.40235e7i	−0.0995508	+	0.172427i
$183$		0			0
$184$	−2.72364e7	−	4.71747e7i	−0.322319	−	0.558274i
$185$	−6.89754e6	−	1.19469e7i	−0.0800927	−	0.138725i
$186$		0			0
$187$	−3.65040e6	+	6.32268e6i	−0.0408221	+	0.0707059i
$188$	3.59255e7			0.394321
$189$		0			0
$190$	1.55626e7			0.164605
$191$	1.05420e7	−	1.82593e7i	0.109473	−	0.189613i	−0.806084	−	0.591801i	$-0.798417\pi$
$191$	1.05420e7	−	1.82593e7i	0.109473	−	0.189613i	0.915557	+	0.402189i	$0.131750\pi$
$192$		0			0
$193$	6.99105e7	+	1.21089e8i	0.699990	+	1.21242i	0.968469	+	0.249133i	$0.0801458\pi$
$193$	6.99105e7	+	1.21089e8i	0.699990	+	1.21242i	−0.268479	+	0.963286i	$0.586521\pi$
$194$	−3.42235e7	−	5.92769e7i	−0.336526	−	0.582880i
$195$		0			0
$196$	2.18052e7	−	3.77678e7i	0.206854	−	0.358282i
$197$	1.45966e8			1.36025			0.680127	−	0.733094i	$-0.261924\pi$
$197$	1.45966e8			1.36025			0.680127	+	0.733094i	$0.261924\pi$
$198$		0			0
$199$	−5.11146e7			−0.459790			−0.229895	−	0.973215i	$-0.573838\pi$
$199$	−5.11146e7			−0.459790			−0.229895	+	0.973215i	$0.573838\pi$
$200$	1.63136e7	−	2.82560e7i	0.144193	−	0.249750i
$201$		0			0
$202$	−7.96024e7	−	1.37875e8i	−0.679511	−	1.17695i
$203$	−3.34052e7	−	5.78595e7i	−0.280271	−	0.485444i
$204$		0			0
$205$	6.72768e6	−	1.16527e7i	0.0545415	−	0.0944686i
$206$	5.59988e7			0.446317
$207$		0			0
$208$	2.19914e7			0.169446
$209$	−4.86330e6	+	8.42348e6i	−0.0368484	+	0.0638234i
$210$		0			0
$211$	−4.90269e7	−	8.49170e7i	−0.359290	−	0.622309i	0.628552	−	0.777768i	$-0.283648\pi$
$211$	−4.90269e7	−	8.49170e7i	−0.359290	−	0.622309i	−0.987842	+	0.155458i	$0.950315\pi$
$212$	5.72083e7	+	9.90877e7i	0.412367	+	0.714240i
$213$		0			0
$214$	1.79225e7	−	3.10427e7i	0.125012	−	0.216527i
$215$	−1.38058e7			−0.0947383
$216$		0			0
$217$	−1.01059e8			−0.671374
$218$	5.88297e6	−	1.01896e7i	0.0384591	−	0.0666131i
$219$		0			0
$220$	−2.30400e6	−	3.99065e6i	−0.0145882	−	0.0252676i
$221$	−3.26650e7	−	5.65774e7i	−0.203568	−	0.352590i
$222$		0			0
$223$	−1.08379e8	+	1.87718e8i	−0.654453	+	1.13355i	0.327578	+	0.944824i	$0.393768\pi$
$223$	−1.08379e8	+	1.87718e8i	−0.654453	+	1.13355i	−0.982031	+	0.188722i	$0.939566\pi$
$224$	1.23535e7			0.0734384
$225$		0			0
$226$	2.78229e7			0.160333
$227$	6.99323e7	−	1.21126e8i	0.396814	−	0.687303i	−0.596516	−	0.802601i	$-0.703449\pi$
$227$	6.99323e7	−	1.21126e8i	0.396814	−	0.687303i	0.993331	+	0.115298i	$0.0367823\pi$
$228$		0			0
$229$	4.74784e7	+	8.22351e7i	0.261260	+	0.452515i	0.966577	−	0.256377i	$-0.0825288\pi$
$229$	4.74784e7	+	8.22351e7i	0.261260	+	0.452515i	−0.705317	+	0.708892i	$0.749195\pi$
$230$	−5.10682e7	−	8.84526e7i	−0.276760	−	0.479362i
$231$		0			0
$232$	−4.53673e7	+	7.85785e7i	−0.238526	+	0.413138i
$233$	−2.10948e8			−1.09252			−0.546261	−	0.837615i	$-0.683949\pi$
$233$	−2.10948e8			−1.09252			−0.546261	+	0.837615i	$0.683949\pi$
$234$		0			0
$235$	6.73603e7			0.338584
$236$	5.71630e7	−	9.90092e7i	0.283089	−	0.490325i
$237$		0			0
$238$	−1.83493e7	−	3.17820e7i	−0.0882269	−	0.152814i
$239$	6.45759e7	+	1.11849e8i	0.305969	+	0.529954i	0.977477	−	0.211043i	$-0.0676862\pi$
$239$	6.45759e7	+	1.11849e8i	0.305969	+	0.529954i	−0.671507	+	0.740998i	$0.734353\pi$
$240$		0			0
$241$	2.00934e7	−	3.48028e7i	0.0924685	−	0.160160i	−0.816081	−	0.577938i	$-0.803858\pi$
$241$	2.00934e7	−	3.48028e7i	0.0924685	−	0.160160i	0.908549	+	0.417778i	$0.137191\pi$
$242$	−1.53017e8			−0.694044
$243$		0			0
$244$	−8.36376e7			−0.368584
$245$	4.08848e7	−	7.08146e7i	0.177616	−	0.307639i
$246$		0			0
$247$	−4.35184e7	−	7.53761e7i	−0.183753	−	0.318269i
$248$	6.86234e7	+	1.18859e8i	0.285687	+	0.494825i
$249$		0			0
$250$	6.80880e7	−	1.17932e8i	0.275601	−	0.477355i
$251$	−2.68201e8			−1.07054			−0.535270	−	0.844681i	$-0.679790\pi$
$251$	−2.68201e8			−1.07054			−0.535270	+	0.844681i	$0.679790\pi$
$252$		0			0
$253$	6.38352e7			0.247821
$254$	−8.41511e7	+	1.45754e8i	−0.322212	+	0.558088i
$255$		0			0
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	8.59320e7	+	1.48839e8i	0.315783	+	0.546952i	0.979604	−	0.200940i	$-0.0643995\pi$
$257$	8.59320e7	+	1.48839e8i	0.315783	+	0.546952i	−0.663821	+	0.747892i	$0.731066\pi$
$258$		0			0
$259$	−2.16698e7	+	3.75331e7i	−0.0775006	+	0.134235i
$260$	4.12339e7			0.145495
$261$		0			0
$262$	−1.65525e8			−0.568602
$263$	−1.01017e8	+	1.74966e8i	−0.342411	+	0.593073i	−0.984880	−	0.173239i	$-0.944577\pi$
$263$	−1.01017e8	+	1.74966e8i	−0.342411	+	0.593073i	0.642469	+	0.766312i	$0.277910\pi$
$264$		0			0
$265$	1.07266e8	+	1.85789e8i	0.354079	+	0.613282i
$266$	−2.44462e7	−	4.23420e7i	−0.0796389	−	0.137939i
$267$		0			0
$268$	6.44421e7	−	1.11617e8i	0.204502	−	0.354208i
$269$	−9.73917e7			−0.305063			−0.152531	−	0.988299i	$-0.548743\pi$
$269$	−9.73917e7			−0.305063			−0.152531	+	0.988299i	$0.548743\pi$
$270$		0			0
$271$	4.51945e8			1.37941			0.689705	−	0.724091i	$-0.257740\pi$
$271$	4.51945e8			1.37941			0.689705	+	0.724091i	$0.257740\pi$
$272$	−2.49201e7	+	4.31628e7i	−0.0750858	+	0.130052i
$273$		0			0
$274$	2.12608e8	+	3.68249e8i	0.624386	+	1.08147i
$275$	1.91175e7	+	3.31125e7i	0.0554328	+	0.0960124i
$276$		0			0
$277$	1.04851e8	−	1.81608e8i	0.296411	−	0.513399i	−0.678901	−	0.734230i	$-0.737543\pi$
$277$	1.04851e8	−	1.81608e8i	0.296411	−	0.513399i	0.975312	+	0.220831i	$0.0708768\pi$
$278$	−1.56007e8			−0.435500
$279$		0			0
$280$	2.31629e7			0.0630579
$281$	−2.66102e8	+	4.60902e8i	−0.715444	+	1.23919i	0.247344	+	0.968928i	$0.420442\pi$
$281$	−2.66102e8	+	4.60902e8i	−0.715444	+	1.23919i	−0.962788	+	0.270258i	$0.912891\pi$
$282$		0			0
$283$	−2.37381e8	−	4.11155e8i	−0.622576	−	1.07833i	−0.989004	−	0.147887i	$-0.952753\pi$
$283$	−2.37381e8	−	4.11155e8i	−0.622576	−	1.07833i	0.366428	−	0.930446i	$-0.380581\pi$
$284$	1.29950e8	+	2.25080e8i	0.336638	+	0.583074i
$285$		0			0
$286$	−1.28856e7	+	2.23185e7i	−0.0325704	+	0.0564136i
$287$	−4.22723e7			−0.105553
$288$		0			0
$289$	−2.62278e8			−0.639176
$290$	−8.50637e7	+	1.47335e8i	−0.204810	+	0.354741i
$291$		0			0
$292$	1.23220e8	+	2.13424e8i	0.289630	+	0.501653i
$293$	1.16059e8	+	2.01020e8i	0.269552	+	0.466878i	0.968746	−	0.248054i	$-0.0797910\pi$
$293$	1.16059e8	+	2.01020e8i	0.269552	+	0.466878i	−0.699194	+	0.714932i	$0.746458\pi$
$294$		0			0
$295$	1.07181e8	−	1.85642e8i	0.243074	−	0.421017i
$296$	5.88590e7			0.131914
$297$		0			0
$298$	6.81251e7			0.149125
$299$	−2.85609e8	+	4.94690e8i	−0.617907	+	1.07025i
$300$		0			0
$301$	2.16865e7	+	3.75622e7i	0.0458361	+	0.0793905i
$302$	−2.54808e8	−	4.41340e8i	−0.532339	−	0.922039i
$303$		0			0
$304$	−3.32001e7	+	5.75043e7i	−0.0677770	+	0.117393i
$305$	−1.56820e8			−0.316485
$306$		0			0
$307$	7.53314e8			1.48591			0.742953	−	0.669343i	$-0.233424\pi$
$307$	7.53314e8			1.48591			0.742953	+	0.669343i	$0.233424\pi$
$308$	−7.23840e6	+	1.25373e7i	−0.0141161	+	0.0244498i
$309$		0			0
$310$	1.28669e8	+	2.22861e8i	0.245306	+	0.424882i
$311$	−2.39889e8	−	4.15500e8i	−0.452219	−	0.783267i	0.546304	−	0.837587i	$-0.316034\pi$
$311$	−2.39889e8	−	4.15500e8i	−0.452219	−	0.783267i	−0.998524	+	0.0543198i	$0.982701\pi$
$312$		0			0
$313$	−3.27762e8	+	5.67701e8i	−0.604163	+	1.04644i	0.388020	+	0.921651i	$0.373159\pi$
$313$	−3.27762e8	+	5.67701e8i	−0.604163	+	1.04644i	−0.992183	+	0.124790i	$0.960174\pi$
$314$	−5.09074e8			−0.927955
$315$		0			0
$316$	6.63828e7			0.118345
$317$	−3.46681e8	+	6.00469e8i	−0.611255	+	1.05872i	0.379775	+	0.925079i	$0.376002\pi$
$317$	−3.46681e8	+	6.00469e8i	−0.611255	+	1.05872i	−0.991029	+	0.133645i	$0.957332\pi$
$318$		0			0
$319$	−5.31648e7	−	9.20841e7i	−0.0916974	−	0.158824i
$320$	−1.57286e7	−	2.72428e7i	−0.0268328	−	0.0464758i
$321$		0			0
$322$	−1.60439e8	+	2.77889e8i	−0.267803	+	0.463848i
$323$	1.97255e8			0.325702
$324$		0			0
$325$	−3.42140e8			−0.552855
$326$	−2.74920e8	+	4.76176e8i	−0.439486	+	0.761212i
$327$		0			0
$328$	2.87048e7	+	4.97181e7i	0.0449154	+	0.0777958i
$329$	−1.05812e8	−	1.83271e8i	−0.163813	−	0.283733i
$330$		0			0
$331$	9.23266e7	−	1.59914e8i	0.139936	−	0.242376i	−0.787536	−	0.616268i	$-0.788644\pi$
$331$	9.23266e7	−	1.59914e8i	0.139936	−	0.242376i	0.927472	+	0.373892i	$0.121977\pi$
$332$	5.89028e8			0.883391
$333$		0			0
$334$	1.03547e8			0.152064
$335$	1.20829e8	−	2.09282e8i	0.175596	−	0.304141i
$336$		0			0
$337$	−4.21941e8	−	7.30824e8i	−0.600548	−	1.04018i	−0.992738	−	0.120295i	$-0.961616\pi$
$337$	−4.21941e8	−	7.30824e8i	−0.600548	−	1.04018i	0.392191	−	0.919884i	$-0.371717\pi$
$338$	1.35689e8	+	2.35021e8i	0.191134	+	0.331053i
$339$		0			0
$340$	−4.67251e7	+	8.09303e7i	−0.0644725	+	0.111670i
$341$	−1.60836e8			−0.219656
$342$		0			0
$343$	−5.67369e8			−0.759165
$344$	2.94523e7	−	5.10129e7i	0.0390090	−	0.0675655i
$345$		0			0
$346$	1.68849e8	+	2.92456e8i	0.219146	+	0.379572i
$347$	−6.11249e7	−	1.05871e8i	−0.0785353	−	0.136027i	0.824083	−	0.566469i	$-0.191691\pi$
$347$	−6.11249e7	−	1.05871e8i	−0.0785353	−	0.136027i	−0.902618	+	0.430442i	$0.858358\pi$
$348$		0			0
$349$	5.26481e8	−	9.11891e8i	0.662969	−	1.14830i	−0.316862	−	0.948472i	$-0.602629\pi$
$349$	5.26481e8	−	9.11891e8i	0.662969	−	1.14830i	0.979832	−	0.199825i	$-0.0640374\pi$
$350$	−1.92195e8			−0.239609
$351$		0			0
$352$	1.96608e7			0.0240271
$353$	3.12292e8	−	5.40906e8i	0.377876	−	0.654501i	−0.612877	−	0.790178i	$-0.709988\pi$
$353$	3.12292e8	−	5.40906e8i	0.377876	−	0.654501i	0.990753	+	0.135678i	$0.0433212\pi$
$354$		0			0
$355$	2.43657e8	+	4.22026e8i	0.289054	+	0.500656i
$356$	4.12577e7	+	7.14605e7i	0.0484652	+	0.0839442i
$357$		0			0
$358$	−4.54559e8	+	7.87319e8i	−0.523600	+	0.906902i
$359$	−7.95194e8			−0.907074			−0.453537	−	0.891237i	$-0.649838\pi$
$359$	−7.95194e8			−0.907074			−0.453537	+	0.891237i	$0.649838\pi$
$360$		0			0
$361$	−6.31075e8			−0.706002
$362$	5.11687e8	−	8.86269e8i	0.566924	−	0.981941i
$363$		0			0
$364$	−6.47716e7	−	1.12188e8i	−0.0703931	−	0.121924i
$365$	2.31038e8	+	4.00170e8i	0.248690	+	0.430744i
$366$		0			0
$367$	5.47225e8	−	9.47821e8i	0.577876	−	1.00091i	−0.417847	−	0.908518i	$-0.637215\pi$
$367$	5.47225e8	−	9.47821e8i	0.577876	−	1.00091i	0.995723	−	0.0923929i	$-0.0294516\pi$
$368$	4.35782e8			0.455829
$369$		0			0
$370$	1.10361e8			0.113268
$371$	3.36993e8	−	5.83689e8i	0.342619	−	0.593434i
$372$		0			0
$373$	−4.41022e8	−	7.63872e8i	−0.440027	−	0.762149i	0.557664	−	0.830067i	$-0.311698\pi$
$373$	−4.41022e8	−	7.63872e8i	−0.440027	−	0.762149i	−0.997691	+	0.0679177i	$0.978364\pi$
$374$	−2.92032e7	−	5.05814e7i	−0.0288655	−	0.0499966i
$375$		0			0
$376$	−1.43702e8	+	2.48899e8i	−0.139414	+	0.241472i
$377$	9.51473e8			0.914538
$378$		0			0
$379$	−1.04251e9			−0.983651			−0.491826	−	0.870694i	$-0.663670\pi$
$379$	−1.04251e9			−0.983651			−0.491826	+	0.870694i	$0.663670\pi$
$380$	−6.22502e7	+	1.07821e8i	−0.0581967	+	0.100800i
$381$		0			0
$382$	8.43361e7	+	1.46074e8i	0.0774090	+	0.134076i
$383$	4.18424e8	+	7.24731e8i	0.380558	+	0.659145i	0.991142	−	0.132806i	$-0.0423987\pi$
$383$	4.18424e8	+	7.24731e8i	0.380558	+	0.659145i	−0.610584	+	0.791951i	$0.709065\pi$
$384$		0			0
$385$	−1.35720e7	+	2.35074e7i	−0.0121208	+	0.0209938i
$386$	−1.11857e9			−0.989936
$387$		0			0
$388$	5.47577e8			0.475920
$389$	7.35299e8	−	1.27358e9i	0.633345	−	1.09699i	−0.353518	−	0.935428i	$-0.615015\pi$
$389$	7.35299e8	−	1.27358e9i	0.633345	−	1.09699i	0.986863	−	0.161558i	$-0.0516519\pi$
$390$		0			0
$391$	−6.47289e8	−	1.12114e9i	−0.547620	−	0.948506i
$392$	1.74442e8	+	3.02142e8i	0.146268	+	0.253344i
$393$		0			0
$394$	−5.83864e8	+	1.01128e9i	−0.480923	+	0.832982i
$395$	1.24468e8			0.101617
$396$		0			0
$397$	−1.26746e9			−1.01664			−0.508322	−	0.861167i	$-0.669734\pi$
$397$	−1.26746e9			−1.01664			−0.508322	+	0.861167i	$0.669734\pi$
$398$	2.04459e8	−	3.54133e8i	0.162560	−	0.281563i
$399$		0			0
$400$	1.30509e8	+	2.26048e8i	0.101960	+	0.176600i
$401$	−2.63929e8	−	4.57139e8i	−0.204401	−	0.354032i	0.745541	−	0.666460i	$-0.232191\pi$
$401$	−2.63929e8	−	4.57139e8i	−0.204401	−	0.354032i	−0.949942	+	0.312428i	$0.898858\pi$
$402$		0			0
$403$	7.19607e8	−	1.24640e9i	0.547681	−	0.948612i
$404$	1.27364e9			0.960974
$405$		0			0
$406$	5.34483e8			0.396363
$407$	−3.44877e7	+	5.97344e7i	−0.0253562	+	0.0439182i
$408$		0			0
$409$	1.11395e8	+	1.92942e8i	0.0805073	+	0.139443i	0.903468	−	0.428656i	$-0.141013\pi$
$409$	1.11395e8	+	1.92942e8i	0.0805073	+	0.139443i	−0.822961	+	0.568098i	$0.807679\pi$
$410$	5.38214e7	+	9.32215e7i	0.0385666	+	0.0667994i
$411$		0			0
$412$	−2.23995e8	+	3.87971e8i	−0.157797	+	0.273312i
$413$	−6.73452e8			−0.470415
$414$		0			0
$415$	1.10443e9			0.758524
$416$	−8.79657e7	+	1.52361e8i	−0.0599083	+	0.103764i
$417$		0			0
$418$	−3.89064e7	−	6.73879e7i	−0.0260558	−	0.0451299i
$419$	2.20291e8	+	3.81554e8i	0.146301	+	0.253400i	0.929858	−	0.367920i	$-0.119930\pi$
$419$	2.20291e8	+	3.81554e8i	0.146301	+	0.253400i	−0.783557	+	0.621320i	$0.786597\pi$
$420$		0			0
$421$	−1.09467e9	+	1.89603e9i	−0.714984	+	1.23839i	0.247981	+	0.968765i	$0.420233\pi$
$421$	−1.09467e9	+	1.89603e9i	−0.714984	+	1.23839i	−0.962966	+	0.269625i	$0.913100\pi$
$422$	7.84430e8			0.508113
$423$		0			0
$424$	−9.15333e8			−0.583175
$425$	3.87703e8	−	6.71521e8i	0.244984	−	0.424325i
$426$		0			0
$427$	2.46339e8	+	4.26671e8i	0.153121	+	0.265214i
$428$	1.43380e8	+	2.48342e8i	0.0883967	+	0.153108i
$429$		0			0
$430$	5.52230e7	−	9.56491e7i	0.0334951	−	0.0580151i
$431$	3.03634e9			1.82675			0.913377	−	0.407114i	$-0.133465\pi$
$431$	3.03634e9			1.82675			0.913377	+	0.407114i	$0.133465\pi$
$432$		0			0
$433$	2.21735e9			1.31258			0.656290	−	0.754509i	$-0.272125\pi$
$433$	2.21735e9			1.31258			0.656290	+	0.754509i	$0.272125\pi$
$434$	4.04234e8	−	7.00155e8i	0.237366	−	0.411131i
$435$		0			0
$436$	4.70637e7	+	8.15168e7i	0.0271947	+	0.0471025i
$437$	−8.62360e8	−	1.49365e9i	−0.494315	−	0.856179i
$438$		0			0
$439$	1.25047e9	−	2.16588e9i	0.705419	−	1.22182i	−0.261121	−	0.965306i	$-0.584092\pi$
$439$	1.25047e9	−	2.16588e9i	0.705419	−	1.22182i	0.966540	−	0.256515i	$-0.0825744\pi$
$440$	3.68640e7			0.0206309
$441$		0			0
$442$	5.22640e8			0.287889
$443$	1.20193e9	−	2.08181e9i	0.656852	−	1.13770i	−0.324573	−	0.945860i	$-0.605221\pi$
$443$	1.20193e9	−	2.08181e9i	0.656852	−	1.13770i	0.981426	−	0.191841i	$-0.0614459\pi$
$444$		0			0
$445$	7.73582e7	+	1.33988e8i	0.0416147	+	0.0720787i
$446$	−8.67033e8	−	1.50174e9i	−0.462768	−	0.801538i
$447$		0			0
$448$	−4.94141e7	+	8.55878e7i	−0.0259644	+	0.0449717i
$449$	2.14935e9			1.12059			0.560294	−	0.828294i	$-0.310688\pi$
$449$	2.14935e9			1.12059			0.560294	+	0.828294i	$0.310688\pi$
$450$		0			0
$451$	−6.72768e7			−0.0345340
$452$	−1.11292e8	+	1.92763e8i	−0.0566863	+	0.0981835i
$453$		0			0
$454$	5.59459e8	+	9.69011e8i	0.280590	+	0.485996i
$455$	−1.21447e8	−	2.10352e8i	−0.0604430	−	0.104690i
$456$		0			0
$457$	−1.15079e9	+	1.99323e9i	−0.564015	+	0.976902i	0.433126	+	0.901334i	$0.357411\pi$
$457$	−1.15079e9	+	1.99323e9i	−0.564015	+	0.976902i	−0.997141	+	0.0755689i	$0.975923\pi$
$458$	−7.59655e8			−0.369477
$459$		0			0
$460$	8.17091e8			0.391397
$461$	−6.89638e8	+	1.19449e9i	−0.327844	+	0.567843i	−0.982084	−	0.188444i	$-0.939656\pi$
$461$	−6.89638e8	+	1.19449e9i	−0.327844	+	0.567843i	0.654239	+	0.756287i	$0.272989\pi$
$462$		0			0
$463$	8.60268e8	+	1.49003e9i	0.402810	+	0.697688i	0.994064	−	0.108798i	$-0.0347001\pi$
$463$	8.60268e8	+	1.49003e9i	0.402810	+	0.697688i	−0.591254	+	0.806486i	$0.701367\pi$
$464$	−3.62938e8	−	6.28628e8i	−0.168663	−	0.292133i
$465$		0			0
$466$	8.43793e8	−	1.46149e9i	0.386265	−	0.669030i
$467$	1.58750e9			0.721280			0.360640	−	0.932705i	$-0.382558\pi$
$467$	1.58750e9			0.721280			0.360640	+	0.932705i	$0.382558\pi$
$468$		0			0
$469$	−7.59209e8			−0.339826
$470$	−2.69441e8	+	4.66686e8i	−0.119708	+	0.207340i
$471$		0			0
$472$	4.57304e8	+	7.92074e8i	0.200174	+	0.346712i
$473$	3.45144e7	+	5.97807e7i	0.0149964	+	0.0259745i
$474$		0			0
$475$	5.16523e8	−	8.94644e8i	0.221137	−	0.383021i
$476$	2.93590e8			0.124772
$477$		0			0
$478$	−1.03321e9			−0.432706
$479$	−8.78348e8	+	1.52134e9i	−0.365168	+	0.632489i	−0.988803	−	0.149226i	$-0.952322\pi$
$479$	−8.78348e8	+	1.52134e9i	−0.365168	+	0.632489i	0.623635	+	0.781715i	$0.285655\pi$
$480$		0			0
$481$	−3.08607e8	−	5.34524e8i	−0.126444	−	0.219008i
$482$	1.60747e8	+	2.78422e8i	0.0653851	+	0.113250i
$483$		0			0
$484$	6.12069e8	−	1.06014e9i	0.245382	−	0.425013i
$485$	1.02671e9			0.408649
$486$		0			0
$487$	1.52004e9			0.596353			0.298177	−	0.954511i	$-0.403622\pi$
$487$	1.52004e9			0.596353			0.298177	+	0.954511i	$0.403622\pi$
$488$	3.34550e8	−	5.79458e8i	0.130314	−	0.225711i
$489$		0			0
$490$	3.27079e8	+	5.66517e8i	0.125593	+	0.217534i
$491$	−1.82412e9	−	3.15946e9i	−0.695453	−	1.20456i	−0.970028	−	0.242994i	$-0.921870\pi$
$491$	−1.82412e9	−	3.15946e9i	−0.695453	−	1.20456i	0.274575	−	0.961566i	$-0.411463\pi$
$492$		0			0
$493$	−1.07818e9	+	1.86747e9i	−0.405255	+	0.701921i
$494$	6.96295e8			0.259866
$495$		0			0
$496$	−1.09797e9			−0.404023
$497$	7.65488e8	−	1.32586e9i	0.279699	−	0.484453i
$498$		0			0
$499$	−2.41752e8	−	4.18726e8i	−0.0870998	−	0.150861i	0.819184	−	0.573530i	$-0.194427\pi$
$499$	−2.41752e8	−	4.18726e8i	−0.0870998	−	0.150861i	−0.906284	+	0.422669i	$0.861093\pi$
$500$	5.44704e8	+	9.43455e8i	0.194879	+	0.337541i
$501$		0			0
$502$	1.07281e9	−	1.85815e9i	0.378493	−	0.655569i
$503$	−4.20389e9			−1.47287			−0.736434	−	0.676510i	$-0.763492\pi$
$503$	−4.20389e9			−1.47287			−0.736434	+	0.676510i	$0.763492\pi$
$504$		0			0
$505$	2.38807e9			0.825140
$506$	−2.55341e8	+	4.42263e8i	−0.0876180	+	0.151759i
$507$		0			0
$508$	−6.73209e8	−	1.16603e9i	−0.227838	−	0.394628i
$509$	1.33886e9	+	2.31897e9i	0.450009	+	0.779439i	0.998386	−	0.0567925i	$-0.0180874\pi$
$509$	1.33886e9	+	2.31897e9i	0.450009	+	0.779439i	−0.548377	+	0.836231i	$0.684754\pi$
$510$		0			0
$511$	7.25845e8	−	1.25720e9i	0.240642	−	0.416804i
$512$	1.34218e8			0.0441942
$513$		0			0
$514$	−1.37491e9			−0.446585
$515$	−4.19991e8	+	7.27445e8i	−0.135492	+	0.234679i
$516$		0			0
$517$	−1.68401e8	−	2.91679e8i	−0.0535954	−	0.0928299i
$518$	−1.73358e8	−	3.00265e8i	−0.0548012	−	0.0949185i
$519$		0			0
$520$	−1.64936e8	+	2.85677e8i	−0.0514402	+	0.0890971i
$521$	−4.83951e9			−1.49923			−0.749616	−	0.661873i	$-0.769762\pi$
$521$	−4.83951e9			−1.49923			−0.749616	+	0.661873i	$0.769762\pi$
$522$		0			0
$523$	6.47019e8			0.197770			0.0988851	−	0.995099i	$-0.468472\pi$
$523$	6.47019e8			0.197770			0.0988851	+	0.995099i	$0.468472\pi$
$524$	6.62099e8	−	1.14679e9i	0.201031	−	0.348196i
$525$		0			0
$526$	−8.08132e8	−	1.39973e9i	−0.242121	−	0.419366i
$527$	1.63088e9	+	2.82476e9i	0.485382	+	0.840707i
$528$		0			0
$529$	−3.95722e9	+	6.85410e9i	−1.16224	+	2.01305i
$530$	−1.71625e9			−0.500743
$531$		0			0
$532$	3.91139e8			0.112626
$533$	3.01008e8	−	5.21360e8i	0.0861058	−	0.149140i
$534$		0			0
$535$	2.68838e8	+	4.65641e8i	0.0759018	+	0.131466i
$536$	5.15537e8	+	8.92937e8i	0.144605	+	0.250463i
$537$		0			0
$538$	3.89567e8	−	6.74750e8i	0.107856	−	0.186812i
$539$	−4.08848e8			−0.112461
$540$		0			0
$541$	−3.47237e8			−0.0942835			−0.0471418	−	0.998888i	$-0.515011\pi$
$541$	−3.47237e8			−0.0942835			−0.0471418	+	0.998888i	$0.515011\pi$
$542$	−1.80778e9	+	3.13117e9i	−0.487695	+	0.844712i
$543$		0			0
$544$	−1.99361e8	−	3.45303e8i	−0.0530937	−	0.0919610i
$545$	8.82445e7	+	1.52844e8i	0.0233507	+	0.0404446i
$546$		0			0
$547$	1.44314e9	−	2.49959e9i	0.377010	−	0.653001i	−0.613615	−	0.789605i	$-0.710285\pi$
$547$	1.44314e9	−	2.49959e9i	0.377010	−	0.653001i	0.990626	+	0.136604i	$0.0436188\pi$
$548$	−3.40173e9			−0.883016
$549$		0			0
$550$	−3.05880e8			−0.0783938
$551$	−1.43642e9	+	2.48796e9i	−0.365807	+	0.633597i
$552$		0			0
$553$	−1.95518e8	−	3.38647e8i	−0.0491642	−	0.0851549i
$554$	8.38811e8	+	1.45286e9i	0.209594	+	0.363028i
$555$		0			0
$556$	6.24029e8	−	1.08085e9i	0.153972	−	0.266688i
$557$	−8.74890e8			−0.214516			−0.107258	−	0.994231i	$-0.534207\pi$
$557$	−8.74890e8			−0.214516			−0.107258	+	0.994231i	$0.534207\pi$
$558$		0			0
$559$	−6.17693e8			−0.149565
$560$	−9.26515e7	+	1.60477e8i	−0.0222943	+	0.0386149i
$561$		0			0
$562$	−2.12881e9	−	3.68722e9i	−0.505895	−	0.876237i
$563$	4.03722e9	+	6.99267e9i	0.953462	+	1.65144i	0.737850	+	0.674965i	$0.235841\pi$
$563$	4.03722e9	+	6.99267e9i	0.953462	+	1.65144i	0.215611	+	0.976479i	$0.430826\pi$
$564$		0			0
$565$	−2.08672e8	+	3.61430e8i	−0.0486737	+	0.0843053i
$566$	3.79809e9			0.880456
$567$		0			0
$568$	−2.07920e9			−0.476078
$569$	−2.75417e9	+	4.77036e9i	−0.626755	+	1.08557i	0.361444	+	0.932394i	$0.382284\pi$
$569$	−2.75417e9	+	4.77036e9i	−0.626755	+	1.08557i	−0.988199	+	0.153178i	$0.951049\pi$
$570$		0			0
$571$	1.40731e9	+	2.43753e9i	0.316347	+	0.547928i	0.979723	−	0.200358i	$-0.0642104\pi$
$571$	1.40731e9	+	2.43753e9i	0.316347	+	0.547928i	−0.663376	+	0.748286i	$0.730877\pi$
$572$	−1.03085e8	−	1.78548e8i	−0.0230308	−	0.0398905i
$573$		0			0
$574$	1.69089e8	−	2.92871e8i	0.0373185	−	0.0646375i
$575$	−6.77983e9			−1.48724
$576$		0			0
$577$	−4.74376e9			−1.02803			−0.514017	−	0.857780i	$-0.671843\pi$
$577$	−4.74376e9			−1.02803			−0.514017	+	0.857780i	$0.671843\pi$
$578$	1.04911e9	−	1.81712e9i	0.225983	−	0.391413i
$579$		0			0
$580$	−6.80509e8	−	1.17868e9i	−0.144823	−	0.250840i
$581$	−1.73487e9	−	3.00489e9i	−0.366987	−	0.635641i
$582$		0			0
$583$	5.36328e8	−	9.28947e8i	0.112096	−	0.194156i
$584$	−1.97153e9			−0.409598
$585$		0			0
$586$	−1.85695e9			−0.381204
$587$	−2.46020e9	+	4.26118e9i	−0.502038	+	0.869555i	0.497960	+	0.867200i	$0.334083\pi$
$587$	−2.46020e9	+	4.26118e9i	−0.502038	+	0.869555i	−0.999997	+	0.00235443i	$0.999251\pi$
$588$		0			0
$589$	2.17276e9	+	3.76333e9i	0.438135	+	0.758873i
$590$	8.57445e8	+	1.48514e9i	0.171880	+	0.297704i
$591$		0			0
$592$	−2.35436e8	+	4.07787e8i	−0.0466388	+	0.0807807i
$593$	−1.96899e9			−0.387750			−0.193875	−	0.981026i	$-0.562106\pi$
$593$	−1.96899e9			−0.387750			−0.193875	+	0.981026i	$0.562106\pi$
$594$		0			0
$595$	5.50480e8			0.107135
$596$	−2.72500e8	+	4.71984e8i	−0.0527236	+	0.0913199i
$597$		0			0
$598$	−2.28487e9	−	3.95752e9i	−0.436926	−	0.756779i
$599$	−4.14421e9	−	7.17799e9i	−0.787858	−	1.36461i	−0.927277	−	0.374377i	$-0.877857\pi$
$599$	−4.14421e9	−	7.17799e9i	−0.787858	−	1.36461i	0.139418	−	0.990234i	$-0.455477\pi$
$600$		0			0
$601$	−3.59672e9	+	6.22971e9i	−0.675844	+	1.17060i	0.300377	+	0.953820i	$0.402887\pi$
$601$	−3.59672e9	+	6.22971e9i	−0.675844	+	1.17060i	−0.976221	+	0.216776i	$0.930446\pi$
$602$	−3.46985e8			−0.0648220
$603$		0			0
$604$	4.07693e9			0.752841
$605$	1.14763e9	−	1.98775e9i	0.210697	−	0.364938i
$606$		0			0
$607$	2.67828e9	+	4.63891e9i	0.486066	+	0.841891i	0.999872	−	0.0160155i	$-0.00509813\pi$
$607$	2.67828e9	+	4.63891e9i	0.486066	+	0.841891i	−0.513806	+	0.857907i	$0.671765\pi$
$608$	−2.65601e8	−	4.60034e8i	−0.0479256	−	0.0830095i
$609$		0			0
$610$	6.27282e8	−	1.08648e9i	0.111894	−	0.193807i
$611$	3.01381e9			0.534530
$612$		0			0
$613$	−1.01444e10			−1.77874			−0.889371	−	0.457187i	$-0.848857\pi$
$613$	−1.01444e10			−1.77874			−0.889371	+	0.457187i	$0.848857\pi$
$614$	−3.01326e9	+	5.21911e9i	−0.525347	+	0.909928i
$615$		0			0
$616$	−5.79072e7	−	1.00298e8i	−0.00998160	−	0.0172886i
$617$	1.20214e9	+	2.08217e9i	0.206043	+	0.356876i	0.950464	−	0.310833i	$-0.100608\pi$
$617$	1.20214e9	+	2.08217e9i	0.206043	+	0.356876i	−0.744422	+	0.667710i	$0.767275\pi$
$618$		0			0
$619$	1.37810e9	−	2.38693e9i	0.233541	−	0.404504i	−0.725307	−	0.688426i	$-0.758302\pi$
$619$	1.37810e9	−	2.38693e9i	0.233541	−	0.404504i	0.958848	+	0.283921i	$0.0916355\pi$
$620$	−2.05870e9			−0.346914
$621$		0			0
$622$	3.83823e9			0.639535
$623$	2.43034e8	−	4.20947e8i	0.0402679	−	0.0697460i
$624$		0			0
$625$	−1.46794e9	−	2.54254e9i	−0.240507	−	0.416570i
$626$	−2.62210e9	−	4.54161e9i	−0.427208	−	0.739945i
$627$		0			0
$628$	2.03630e9	−	3.52697e9i	0.328082	−	0.568254i
$629$	1.39882e9			0.224122
$630$		0			0
$631$	3.92975e9			0.622676			0.311338	−	0.950299i	$-0.399223\pi$
$631$	3.92975e9			0.622676			0.311338	+	0.950299i	$0.399223\pi$
$632$	−2.65531e8	+	4.59913e8i	−0.0418413	+	0.0724713i
$633$		0			0
$634$	−2.77345e9	−	4.80375e9i	−0.432222	−	0.748631i
$635$	−1.26227e9	−	2.18631e9i	−0.195633	−	0.338847i
$636$		0			0
$637$	1.82926e9	−	3.16836e9i	0.280405	−	0.485676i
$638$	8.50637e8			0.129680
$639$		0			0
$640$	2.51658e8			0.0379473
$641$	−6.09930e9	+	1.05643e10i	−0.914696	+	1.58430i	−0.107349	+	0.994221i	$0.534236\pi$
$641$	−6.09930e9	+	1.05643e10i	−0.914696	+	1.58430i	−0.807346	+	0.590078i	$0.799097\pi$
$642$		0			0
$643$	−2.32291e8	−	4.02340e8i	−0.0344583	−	0.0596835i	0.848282	−	0.529545i	$-0.177637\pi$
$643$	−2.32291e8	−	4.02340e8i	−0.0344583	−	0.0596835i	−0.882740	+	0.469861i	$0.844304\pi$
$644$	−1.28351e9	−	2.22311e9i	−0.189365	−	0.327990i
$645$		0			0
$646$	−7.89022e8	+	1.36663e9i	−0.115153	+	0.199451i
$647$	6.98889e9			1.01448			0.507239	−	0.861805i	$-0.330666\pi$
$647$	6.98889e9			1.01448			0.507239	+	0.861805i	$0.330666\pi$
$648$		0			0
$649$	−1.07181e9			−0.153908
$650$	1.36856e9	−	2.37041e9i	0.195464	−	0.338553i
$651$		0			0
$652$	−2.19936e9	−	3.80941e9i	−0.310764	−	0.538258i
$653$	−1.72494e9	−	2.98768e9i	−0.242425	−	0.419892i	0.718980	−	0.695031i	$-0.244609\pi$
$653$	−1.72494e9	−	2.98768e9i	−0.242425	−	0.419892i	−0.961404	+	0.275139i	$0.911276\pi$
$654$		0			0
$655$	1.24144e9	−	2.15023e9i	0.172615	−	0.298979i
$656$	−4.59276e8			−0.0635200
$657$		0			0
$658$	1.69299e9			0.231667
$659$	4.93727e9	−	8.55160e9i	0.672029	−	1.16399i	−0.305299	−	0.952256i	$-0.598757\pi$
$659$	4.93727e9	−	8.55160e9i	0.672029	−	1.16399i	0.977328	−	0.211731i	$-0.0679101\pi$
$660$		0			0
$661$	6.14124e9	+	1.06369e10i	0.827087	+	1.43256i	0.900314	+	0.435241i	$0.143337\pi$
$661$	6.14124e9	+	1.06369e10i	0.827087	+	1.43256i	−0.0732275	+	0.997315i	$0.523330\pi$
$662$	7.38613e8	+	1.27932e9i	0.0989496	+	0.171386i
$663$		0			0
$664$	−2.35611e9	+	4.08091e9i	−0.312326	+	0.540964i
$665$	7.33386e8			0.0967067
$666$		0			0
$667$	1.88544e10			2.46021
$668$	−4.14189e8	+	7.17397e8i	−0.0537627	+	0.0931198i
$669$		0			0
$670$	9.66632e8	+	1.67426e9i	0.124165	+	0.215060i
$671$	3.92051e8	+	6.79052e8i	0.0500972	+	0.0867710i
$672$		0			0
$673$	−4.60616e9	+	7.97811e9i	−0.582488	+	1.00890i	0.412696	+	0.910869i	$0.364587\pi$
$673$	−4.60616e9	+	7.97811e9i	−0.582488	+	1.00890i	−0.995184	+	0.0980294i	$0.968746\pi$
$674$	6.75106e9			0.849303
$675$		0			0
$676$	−2.17103e9			−0.270304
$677$	−1.87113e9	+	3.24089e9i	−0.231763	+	0.401425i	−0.958327	−	0.285674i	$-0.907783\pi$
$677$	−1.87113e9	+	3.24089e9i	−0.231763	+	0.401425i	0.726564	+	0.687099i	$0.241116\pi$
$678$		0			0
$679$	−1.61278e9	−	2.79342e9i	−0.197712	−	0.342446i
$680$	−3.73801e8	−	6.47442e8i	−0.0455889	−	0.0789623i
$681$		0			0
$682$	6.43344e8	−	1.11430e9i	0.0776601	−	0.134511i
$683$	−4.17620e9			−0.501544			−0.250772	−	0.968046i	$-0.580684\pi$
$683$	−4.17620e9			−0.501544			−0.250772	+	0.968046i	$0.580684\pi$
$684$		0			0
$685$	−6.37825e9			−0.758202
$686$	2.26948e9	−	3.93085e9i	0.268405	−	0.464892i
$687$		0			0
$688$	2.35618e8	+	4.08103e8i	0.0275835	+	0.0477760i
$689$	4.79924e9	+	8.31253e9i	0.558992	+	0.968202i
$690$		0			0
$691$	3.47365e9	−	6.01654e9i	0.400510	−	0.693703i	−0.593278	−	0.804998i	$-0.702166\pi$
$691$	3.47365e9	−	6.01654e9i	0.400510	−	0.693703i	0.993787	+	0.111294i	$0.0354997\pi$
$692$	−2.70159e9			−0.309919
$693$		0			0
$694$	9.77998e8			0.111066
$695$	1.17005e9	−	2.02659e9i	0.132208	−	0.228992i
$696$		0			0
$697$	6.82187e8	+	1.18158e9i	0.0763112	+	0.132175i
$698$	4.21185e9	+	7.29513e9i	0.468790	+	0.811968i
$699$		0			0
$700$	7.68778e8	−	1.33156e9i	0.0847146	−	0.146730i
$701$	9.64715e9			1.05776			0.528879	−	0.848697i	$-0.322613\pi$
$701$	9.64715e9			1.05776			0.528879	+	0.848697i	$0.322613\pi$
$702$		0			0
$703$	1.86360e9			0.202306
$704$	−7.86432e7	+	1.36214e8i	−0.00849487	+	0.0147136i
$705$		0			0
$706$	2.49834e9	+	4.32725e9i	0.267199	+	0.462802i
$707$	−3.75126e9	−	6.49738e9i	−0.399218	−	0.691465i
$708$		0			0
$709$	−3.86203e9	+	6.68924e9i	−0.406962	+	0.704879i	−0.994548	−	0.104283i	$-0.966745\pi$
$709$	−3.86203e9	+	6.68924e9i	−0.406962	+	0.704879i	0.587585	+	0.809162i	$0.300079\pi$
$710$	−3.89851e9			−0.408784
$711$		0			0
$712$	−6.60124e8			−0.0685402
$713$	1.42597e10	−	2.46986e10i	1.47332	−	2.55187i
$714$		0			0
$715$	−1.93284e8	−	3.34778e8i	−0.0197754	−	0.0342520i
$716$	−3.63647e9	−	6.29855e9i	−0.370241	−	0.641277i
$717$		0			0
$718$	3.18078e9	−	5.50927e9i	0.320699	−	0.555467i
$719$	1.11572e9			0.111945			0.0559725	−	0.998432i	$-0.482174\pi$
$719$	1.11572e9			0.111945			0.0559725	+	0.998432i	$0.482174\pi$
$720$		0			0
$721$	2.63894e9			0.262214
$722$	2.52430e9	−	4.37222e9i	0.249609	−	0.432336i
$723$		0			0
$724$	4.09350e9	+	7.09015e9i	0.400876	+	0.694337i
$725$	5.64654e9	+	9.78010e9i	0.550300	+	0.953148i
$726$		0			0
$727$	3.92513e9	−	6.79852e9i	0.378864	−	0.656212i	−0.612033	−	0.790832i	$-0.709648\pi$
$727$	3.92513e9	−	6.79852e9i	0.378864	−	0.656212i	0.990897	+	0.134620i	$0.0429814\pi$
$728$	1.03635e9			0.0995508
$729$		0			0
$730$	−3.69661e9			−0.351701
$731$	6.99952e8	−	1.21235e9i	0.0662762	−	0.114794i
$732$		0			0
$733$	7.18261e9	+	1.24406e10i	0.673625	+	1.16675i	0.976869	+	0.213840i	$0.0685971\pi$
$733$	7.18261e9	+	1.24406e10i	0.673625	+	1.16675i	−0.303244	+	0.952913i	$0.598070\pi$
$734$	4.37780e9	+	7.58257e9i	0.408620	+	0.707751i
$735$		0			0
$736$	−1.74313e9	+	3.01918e9i	−0.161160	+	0.279137i
$737$	−1.20829e9			−0.111182
$738$		0			0
$739$	5.13869e9			0.468379			0.234189	−	0.972191i	$-0.424756\pi$
$739$	5.13869e9			0.468379			0.234189	+	0.972191i	$0.424756\pi$
$740$	−4.41443e8	+	7.64601e8i	−0.0400464	+	0.0693624i
$741$		0			0
$742$	2.69594e9	+	4.66951e9i	0.242268	+	0.419621i
$743$	5.60912e9	+	9.71528e9i	0.501688	+	0.868949i	0.999998	+	0.00195014i	$0.000620748\pi$
$743$	5.60912e9	+	9.71528e9i	0.501688	+	0.868949i	−0.498310	+	0.866999i	$0.666046\pi$
$744$		0			0
$745$	−5.10938e8	+	8.84970e8i	−0.0452711	+	0.0784119i
$746$	7.05635e9			0.622292
$747$		0			0
$748$	4.67251e8			0.0408221
$749$	8.44599e8	−	1.46289e9i	0.0734453	−	0.127211i
$750$		0			0
$751$	−1.08170e10	−	1.87357e10i	−0.931899	−	1.61410i	−0.780072	−	0.625690i	$-0.784817\pi$
$751$	−1.08170e10	−	1.87357e10i	−0.931899	−	1.61410i	−0.151828	−	0.988407i	$-0.548516\pi$
$752$	−1.14962e9	−	1.99119e9i	−0.0985804	−	0.170746i
$753$		0			0
$754$	−3.80589e9	+	6.59200e9i	−0.323338	+	0.560038i
$755$	7.64424e9			0.646427
$756$		0			0
$757$	−1.67963e10			−1.40727			−0.703635	−	0.710561i	$-0.748441\pi$
$757$	−1.67963e10			−1.40727			−0.703635	+	0.710561i	$0.748441\pi$
$758$	4.17002e9	−	7.22269e9i	0.347773	−	0.602361i
$759$		0			0
$760$	−4.98002e8	−	8.62565e8i	−0.0411513	−	0.0712761i
$761$	−1.20607e10	−	2.08897e10i	−0.992030	−	1.71825i	−0.605136	−	0.796122i	$-0.706881\pi$
$761$	−1.20607e10	−	2.08897e10i	−0.992030	−	1.71825i	−0.386894	−	0.922124i	$-0.626452\pi$
$762$		0			0
$763$	2.77235e8	−	4.80185e8i	0.0225950	−	0.0391357i
$764$	−1.34938e9			−0.109473
$765$		0			0
$766$	−6.69478e9			−0.538190
$767$	4.79544e9	−	8.30595e9i	0.383747	−	0.664669i
$768$		0			0
$769$	−8.33515e9	−	1.44369e10i	−0.660954	−	1.14481i	−0.980365	−	0.197190i	$-0.936818\pi$
$769$	−8.33515e9	−	1.44369e10i	−0.660954	−	1.14481i	0.319411	−	0.947616i	$-0.396515\pi$
$770$	−1.08576e8	−	1.88059e8i	−0.00857070	−	0.0148449i
$771$		0			0
$772$	4.47428e9	−	7.74967e9i	0.349995	−	0.606210i
$773$	−1.34400e10			−1.04658			−0.523288	−	0.852156i	$-0.675295\pi$
$773$	−1.34400e10			−1.04658			−0.523288	+	0.852156i	$0.675295\pi$
$774$		0			0
$775$	1.70821e10			1.31821
$776$	−2.19031e9	+	3.79372e9i	−0.168263	+	0.291440i
$777$		0			0
$778$	5.88239e9	+	1.01886e10i	0.447843	+	0.775686i
$779$	9.08854e8	+	1.57418e9i	0.0688831	+	0.119309i
$780$		0			0
$781$	1.21828e9	−	2.11013e9i	0.0915102	−	0.158500i
$782$	1.03566e10			0.774452
$783$		0			0
$784$	−2.79107e9			−0.206854
$785$	3.81805e9	−	6.61306e9i	0.281707	−	0.487932i
$786$		0			0
$787$	−9.40811e9	−	1.62953e10i	−0.688004	−	1.19166i	−0.972483	−	0.232976i	$-0.925154\pi$
$787$	−9.40811e9	−	1.62953e10i	−0.688004	−	1.19166i	0.284479	−	0.958682i	$-0.408180\pi$
$788$	−4.67092e9	−	8.09026e9i	−0.340064	−	0.589008i
$789$		0			0
$790$	−4.97871e8	+	8.62338e8i	−0.0359271	+	0.0622275i
$791$	1.31115e9			0.0941968
$792$		0			0
$793$	−7.01641e9			−0.499642
$794$	5.06985e9	−	8.78125e9i	0.359438	−	0.622565i
$795$		0			0
$796$	1.63567e9	+	2.83306e9i	0.114948	+	0.199095i
$797$	−2.89472e9	−	5.01380e9i	−0.202536	−	0.350803i	0.746809	−	0.665039i	$-0.231585\pi$
$797$	−2.89472e9	−	5.01380e9i	−0.202536	−	0.350803i	−0.949345	+	0.314236i	$0.898252\pi$
$798$		0			0
$799$	−3.41517e9	+	5.91524e9i	−0.236864	+	0.410260i
$800$	−2.08814e9			−0.144193
$801$		0			0
$802$	4.22287e9			0.289066
$803$	1.15519e9	−	2.00085e9i	0.0787317	−	0.136367i
$804$		0			0
$805$	−2.40659e9	−	4.16833e9i	−0.162598	−	0.281629i
$806$	5.75686e9	+	9.97117e9i	0.387269	+	0.670770i
$807$		0			0
$808$	−5.09456e9	+	8.82403e9i	−0.339756	+	0.588474i
$809$	2.81286e10			1.86779			0.933897	−	0.357543i	$-0.116385\pi$
$809$	2.81286e10			1.86779			0.933897	+	0.357543i	$0.116385\pi$
$810$		0			0
$811$	6.63925e9			0.437065			0.218532	−	0.975830i	$-0.429873\pi$
$811$	6.63925e9			0.437065			0.218532	+	0.975830i	$0.429873\pi$
$812$	−2.13793e9	+	3.70301e9i	−0.140135	+	0.242722i
$813$		0			0
$814$	−2.75902e8	−	4.77876e8i	−0.0179295	−	0.0310548i
$815$	−4.12380e9	−	7.14264e9i	−0.266837	−	0.462176i
$816$		0			0
$817$	9.32522e8	−	1.61517e9i	0.0598249	−	0.103620i
$818$	−1.78233e9			−0.113855
$819$		0			0
$820$	−8.61143e8			−0.0545415
$821$	−2.67600e9	+	4.63496e9i	−0.168766	+	0.292311i	−0.937986	−	0.346673i	$-0.887312\pi$
$821$	−2.67600e9	+	4.63496e9i	−0.168766	+	0.292311i	0.769220	+	0.638984i	$0.220645\pi$
$822$		0			0
$823$	−5.52794e8	−	9.57467e8i	−0.0345672	−	0.0598721i	0.848224	−	0.529637i	$-0.177672\pi$
$823$	−5.52794e8	−	9.57467e8i	−0.0345672	−	0.0598721i	−0.882791	+	0.469765i	$0.844339\pi$
$824$	−1.79196e9	−	3.10377e9i	−0.111579	−	0.193261i
$825$		0			0
$826$	2.69381e9	−	4.66581e9i	0.166317	−	0.288069i
$827$	9.56978e9			0.588346			0.294173	−	0.955752i	$-0.404956\pi$
$827$	9.56978e9			0.588346			0.294173	+	0.955752i	$0.404956\pi$
$828$		0			0
$829$	−2.36632e10			−1.44256			−0.721278	−	0.692646i	$-0.756445\pi$
$829$	−2.36632e10			−1.44256			−0.721278	+	0.692646i	$0.756445\pi$
$830$	−4.41771e9	+	7.65170e9i	−0.268179	+	0.464499i
$831$		0			0
$832$	−7.03726e8	−	1.21889e9i	−0.0423615	−	0.0733723i
$833$	4.14572e9	+	7.18060e9i	0.248509	+	0.430431i
$834$		0			0
$835$	−7.76605e8	+	1.34512e9i	−0.0461634	+	0.0799573i
$836$	6.22502e8			0.0368484
$837$		0			0
$838$	−3.52465e9			−0.206901
$839$	−1.03620e10	+	1.79475e10i	−0.605726	+	1.04915i	0.386210	+	0.922411i	$0.373784\pi$
$839$	−1.03620e10	+	1.79475e10i	−0.605726	+	1.04915i	−0.991936	+	0.126737i	$0.959549\pi$
$840$		0			0
$841$	−7.07782e9	−	1.22591e10i	−0.410311	−	0.710680i
$842$	−8.75737e9	−	1.51682e10i	−0.505570	−	0.875674i
$843$		0			0
$844$	−3.13772e9	+	5.43469e9i	−0.179645	+	0.311155i
$845$	−4.07068e9			−0.232097
$846$		0			0
$847$	−7.21094e9			−0.407756
$848$	3.66133e9	−	6.34161e9i	0.206183	−	0.357120i
$849$		0			0
$850$	3.10162e9	+	5.37217e9i	0.173230	+	0.300043i
$851$	−6.11536e9	−	1.05921e10i	−0.340148	−	0.589154i
$852$		0			0
$853$	9.81270e9	−	1.69961e10i	0.541336	−	0.937622i	−0.457492	−	0.889214i	$-0.651252\pi$
$853$	9.81270e9	−	1.69961e10i	0.541336	−	0.937622i	0.998828	−	0.0484076i	$-0.0154147\pi$
$854$	−3.94142e9			−0.216546
$855$		0			0
$856$	−2.29408e9			−0.125012
$857$	−1.17043e10	+	2.02724e10i	−0.635202	+	1.10020i	0.351271	+	0.936274i	$0.385750\pi$
$857$	−1.17043e10	+	2.02724e10i	−0.635202	+	1.10020i	−0.986472	+	0.163928i	$0.947584\pi$
$858$		0			0
$859$	−3.18993e9	−	5.52512e9i	−0.171714	−	0.297417i	0.767305	−	0.641282i	$-0.221597\pi$
$859$	−3.18993e9	−	5.52512e9i	−0.171714	−	0.297417i	−0.939019	+	0.343865i	$0.888264\pi$
$860$	4.41784e8	+	7.65193e8i	0.0236846	+	0.0410229i
$861$		0			0
$862$	−1.21454e10	+	2.10364e10i	−0.645855	+	1.11865i
$863$	1.63727e9			0.0867127			0.0433564	−	0.999060i	$-0.486195\pi$
$863$	1.63727e9			0.0867127			0.0433564	+	0.999060i	$0.486195\pi$
$864$		0			0
$865$	−5.06548e9			−0.266112
$866$	−8.86939e9	+	1.53622e10i	−0.464067	+	0.803788i
$867$		0			0
$868$	3.23388e9	+	5.60124e9i	0.167843	+	0.290713i
$869$	−3.11169e8	−	5.38961e8i	−0.0160852	−	0.0278605i
$870$		0			0
$871$	5.40609e9	−	9.36363e9i	0.277217	−	0.480154i
$872$	−7.53020e8			−0.0384591
$873$		0			0
$874$	1.37978e10			0.699067
$875$	3.20865e9	−	5.55754e9i	0.161917	−	0.280449i
$876$		0			0
$877$	1.65888e10	+	2.87326e10i	0.830455	+	1.43839i	0.897678	+	0.440653i	$0.145253\pi$
$877$	1.65888e10	+	2.87326e10i	0.830455	+	1.43839i	−0.0672222	+	0.997738i	$0.521414\pi$
$878$	1.00037e10	+	1.73270e10i	0.498806	+	0.863958i
$879$		0			0
$880$	−1.47456e8	+	2.55401e8i	−0.00729412	+	0.0126338i
$881$	−5.88175e9			−0.289795			−0.144897	−	0.989447i	$-0.546285\pi$
$881$	−5.88175e9			−0.289795			−0.144897	+	0.989447i	$0.546285\pi$
$882$		0			0
$883$	5.84882e9			0.285894			0.142947	−	0.989730i	$-0.454342\pi$
$883$	5.84882e9			0.285894			0.142947	+	0.989730i	$0.454342\pi$
$884$	−2.09056e9	+	3.62096e9i	−0.101784	+	0.176295i
$885$		0			0
$886$	9.61548e9	+	1.66545e10i	0.464465	+	0.804477i
$887$	3.90548e9	+	6.76448e9i	0.187906	+	0.325463i	0.944552	−	0.328362i	$-0.106497\pi$
$887$	3.90548e9	+	6.76448e9i	0.187906	+	0.325463i	−0.756646	+	0.653825i	$0.773163\pi$
$888$		0			0
$889$	−3.96562e9	+	6.86866e9i	−0.189302	+	0.327880i
$890$	−1.23773e9			−0.0588520
$891$		0			0
$892$	1.38725e10			0.654453
$893$	−4.54991e9	+	7.88067e9i	−0.213807	+	0.370325i
$894$		0			0
$895$	−6.81839e9	−	1.18098e10i	−0.317908	−	0.550632i
$896$	−3.95313e8	−	6.84702e8i	−0.0183596	−	0.0317998i
$897$		0			0
$898$	−8.59741e9	+	1.48912e10i	−0.396187	+	0.686217i
$899$	−4.75045e10			−2.18060
$900$		0			0
$901$	−2.17535e10			−0.990813
$902$	2.69107e8	−	4.66107e8i	0.0122096	−	0.0211477i
$903$		0			0
$904$	−8.90333e8	−	1.54210e9i	−0.0400833	−	0.0694262i
$905$	7.67531e9	+	1.32940e10i	0.344212	+	0.596193i
$906$		0			0
$907$	2.06350e10	−	3.57409e10i	0.918289	−	1.59052i	0.116276	−	0.993217i	$-0.462904\pi$
$907$	2.06350e10	−	3.57409e10i	0.918289	−	1.59052i	0.802013	−	0.597307i	$-0.203763\pi$
$908$	−8.95134e9			−0.396814
$909$		0			0
$910$	1.94315e9			0.0854793
$911$	−3.33211e9	+	5.77138e9i	−0.146017	+	0.252910i	−0.929752	−	0.368186i	$-0.879979\pi$
$911$	−3.33211e9	+	5.77138e9i	−0.146017	+	0.252910i	0.783735	+	0.621096i	$0.213312\pi$
$912$		0			0
$913$	−2.76107e9	−	4.78231e9i	−0.120069	−	0.207965i
$914$	−9.20634e9	−	1.59459e10i	−0.398819	−	0.690774i
$915$		0			0
$916$	3.03862e9	−	5.26304e9i	0.130630	−	0.226257i
$917$	−7.80035e9			−0.334058
$918$		0			0
$919$	5.45018e9			0.231636			0.115818	−	0.993270i	$-0.463051\pi$
$919$	5.45018e9			0.231636			0.115818	+	0.993270i	$0.463051\pi$
$920$	−3.26836e9	+	5.66097e9i	−0.138380	+	0.239681i
$921$		0			0
$922$	−5.51710e9	−	9.55590e9i	−0.231821	−	0.401526i
$923$	1.09016e10	+	1.88821e10i	0.456336	+	0.790397i
$924$		0			0
$925$	3.66288e9	−	6.34430e9i	0.152169	−	0.263565i
$926$	−1.37643e10			−0.569660
$927$		0			0
$928$	5.80701e9			0.238526
$929$	−3.89178e9	+	6.74076e9i	−0.159255	+	0.275838i	−0.934600	−	0.355700i	$-0.884243\pi$
$929$	−3.89178e9	+	6.74076e9i	−0.159255	+	0.275838i	0.775345	+	0.631538i	$0.217576\pi$
$930$		0			0
$931$	5.52320e9	+	9.56647e9i	0.224319	+	0.388533i
$932$	6.75034e9	+	1.16919e10i	0.273130	+	0.473076i
$933$		0			0
$934$	−6.34998e9	+	1.09985e10i	−0.255011	+	0.441692i
$935$	8.76096e8			0.0350519
$936$		0			0
$937$	4.59669e10			1.82539			0.912697	−	0.408638i	$-0.133996\pi$
$937$	4.59669e10			1.82539			0.912697	+	0.408638i	$0.133996\pi$
$938$	3.03684e9	−	5.25995e9i	0.120147	−	0.208100i
$939$		0			0
$940$	−2.15553e9	−	3.73349e9i	−0.0846460	−	0.146611i
$941$	8.15759e9	+	1.41294e10i	0.319152	+	0.552788i	0.980311	−	0.197458i	$-0.0632685\pi$
$941$	8.15759e9	+	1.41294e10i	0.319152	+	0.552788i	−0.661159	+	0.750246i	$0.729935\pi$
$942$		0			0
$943$	5.96476e9	−	1.03313e10i	0.231634	−	0.401202i
$944$	−7.31687e9			−0.283089
$945$		0			0
$946$	−5.52230e8			−0.0212081
$947$	−1.56967e10	+	2.71875e10i	−0.600597	+	1.04027i	0.392133	+	0.919908i	$0.371737\pi$
$947$	−1.56967e10	+	2.71875e10i	−0.600597	+	1.04027i	−0.992731	+	0.120357i	$0.961596\pi$
$948$		0			0
$949$	1.03370e10	+	1.79043e10i	0.392613	+	0.680025i
$950$	4.13218e9	+	7.15715e9i	0.156368	+	0.270837i
$951$		0			0
$952$	−1.17436e9	+	2.03405e9i	−0.0441135	+	0.0764068i
$953$	−4.82350e10			−1.80525			−0.902625	−	0.430428i	$-0.858363\pi$
$953$	−4.82350e10			−1.80525			−0.902625	+	0.430428i	$0.858363\pi$
$954$		0			0
$955$	−2.53008e9			−0.0939989
$956$	4.13286e9	−	7.15832e9i	0.152985	−	0.264977i
$957$		0			0
$958$	−7.02679e9	−	1.21708e10i	−0.258213	−	0.447237i
$959$	1.00192e10	+	1.73537e10i	0.366832	+	0.635371i
$960$		0			0
$961$	−2.21718e10	+	3.84026e10i	−0.805877	+	1.39582i
$962$	4.93772e9			0.178819
$963$		0			0
$964$	−2.57195e9			−0.0924685
$965$	8.38927e9	−	1.45306e10i	0.300523	−	0.520522i
$966$		0			0
$967$	−1.61119e9	−	2.79066e9i	−0.0572999	−	0.0992463i	0.835953	−	0.548802i	$-0.184916\pi$
$967$	−1.61119e9	−	2.79066e9i	−0.0572999	−	0.0992463i	−0.893252	+	0.449555i	$0.851582\pi$
$968$	4.89656e9	+	8.48108e9i	0.173511	+	0.300530i
$969$		0			0
$970$	−4.10682e9	+	7.11323e9i	−0.144479	+	0.250245i
$971$	2.25397e10			0.790096			0.395048	−	0.918660i	$-0.370728\pi$
$971$	2.25397e10			0.790096			0.395048	+	0.918660i	$0.370728\pi$
$972$		0			0
$973$	−7.35184e9			−0.255859
$974$	−6.08016e9	+	1.05311e10i	−0.210843	+	0.365190i
$975$		0			0
$976$	2.67640e9	+	4.63566e9i	0.0921461	+	0.159602i
$977$	−2.15788e10	−	3.73756e10i	−0.740280	−	1.28220i	−0.952368	−	0.304952i	$-0.901359\pi$
$977$	−2.15788e10	−	3.73756e10i	−0.740280	−	1.28220i	0.212087	−	0.977251i	$-0.431974\pi$
$978$		0			0
$979$	3.86791e8	−	6.69942e8i	0.0131746	−	0.0228191i
$980$	−5.23326e9			−0.177616
$981$		0			0
$982$	2.91859e10			0.983519
$983$	1.14330e10	−	1.98025e10i	0.383903	−	0.664940i	−0.607713	−	0.794157i	$-0.707913\pi$
$983$	1.14330e10	−	1.98025e10i	0.383903	−	0.664940i	0.991616	+	0.129217i	$0.0412463\pi$
$984$		0			0
$985$	−8.75797e9	−	1.51692e10i	−0.291996	−	0.505751i
$986$	−8.62546e9	−	1.49397e10i	−0.286558	−	0.496333i
$987$		0			0
$988$	−2.78518e9	+	4.82407e9i	−0.0918764	+	0.159135i
$989$	−1.22402e10			−0.402347
$990$		0			0
$991$	1.13727e10			0.371198			0.185599	−	0.982626i	$-0.440577\pi$
$991$	1.13727e10			0.371198			0.185599	+	0.982626i	$0.440577\pi$
$992$	4.39190e9	−	7.60699e9i	0.142844	−	0.247413i
$993$		0			0
$994$	6.12390e9	+	1.06069e10i	0.197777	+	0.342560i
$995$	3.06688e9	+	5.31199e9i	0.0986997	+	0.170953i
$996$		0			0
$997$	2.15768e10	−	3.73721e10i	0.689530	−	1.19430i	−0.282460	−	0.959279i	$-0.591150\pi$
$997$	2.15768e10	−	3.73721e10i	0.689530	−	1.19430i	0.971990	−	0.235022i	$-0.0755164\pi$
$998$	3.86802e9			0.123178
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.8.c.b.55.1		2
3.2	odd	2		162.8.c.k.55.1		2
9.2	odd	6		54.8.a.a.1.1	✓	1
9.4	even	3	inner	162.8.c.b.109.1		2
9.5	odd	6		162.8.c.k.109.1		2
9.7	even	3		54.8.a.f.1.1	yes	1
36.7	odd	6		432.8.a.g.1.1		1
36.11	even	6		432.8.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.8.a.a.1.1	✓	1	9.2	odd	6
54.8.a.f.1.1	yes	1	9.7	even	3
162.8.c.b.55.1		2	1.1	even	1	trivial
162.8.c.b.109.1		2	9.4	even	3	inner
162.8.c.k.55.1		2	3.2	odd	2
162.8.c.k.109.1		2	9.5	odd	6
432.8.a.b.1.1		1	36.11	even	6
432.8.a.g.1.1		1	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	162.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 + 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-60.0000 - 103.923i) q^{5} +(-188.500 + 326.492i) q^{7} +512.000 q^{8} +960.000 q^{10} +(-300.000 + 519.615i) q^{11} +(-2684.50 - 4649.69i) q^{13} +(-1508.00 - 2611.93i) q^{14} +(-2048.00 + 3547.24i) q^{16} +12168.0 q^{17} +16211.0 q^{19} +(-3840.00 + 6651.08i) q^{20} +(-2400.00 - 4156.92i) q^{22} +(-53196.0 - 92138.2i) q^{23} +(31862.5 - 55187.5i) q^{25} +42952.0 q^{26} +24128.0 q^{28} +(-88608.0 + 153474. i) q^{29} +(134030. + 232147. i) q^{31} +(-16384.0 - 28377.9i) q^{32} +(-48672.0 + 84302.4i) q^{34} +45240.0 q^{35} +114959. q^{37} +(-64844.0 + 112313. i) q^{38} +(-30720.0 - 53208.6i) q^{40} +(56064.0 + 97105.7i) q^{41} +(57524.0 - 99634.5i) q^{43} +38400.0 q^{44} +851136. q^{46} +(-280668. + 486131. i) q^{47} +(340707. + 590122. i) q^{49} +(254900. + 441500. i) q^{50} +(-171808. + 297580. i) q^{52} -1.78776e6 q^{53} +72000.0 q^{55} +(-96512.0 + 167164. i) q^{56} +(-708864. - 1.22779e6i) q^{58} +(893172. + 1.54702e6i) q^{59} +(653419. - 1.13175e6i) q^{61} -2.14448e6 q^{62} +262144. q^{64} +(-322140. + 557963. i) q^{65} +(1.00691e6 + 1.74402e6i) q^{67} +(-389376. - 674419. i) q^{68} +(-180960. + 313432. i) q^{70} -4.06094e6 q^{71} -3.85064e6 q^{73} +(-459836. + 796459. i) q^{74} +(-518752. - 898505. i) q^{76} +(-113100. - 195895. i) q^{77} +(-518616. + 898268. i) q^{79} +491520. q^{80} -897024. q^{82} +(-4.60178e6 + 7.97052e6i) q^{83} +(-730080. - 1.26454e6i) q^{85} +(460192. + 797076. i) q^{86} +(-153600. + 266043. i) q^{88} -1.28930e6 q^{89} +2.02411e6 q^{91} +(-3.40454e6 + 5.89684e6i) q^{92} +(-2.24534e6 - 3.88905e6i) q^{94} +(-972660. - 1.68470e6i) q^{95} +(-4.27794e6 + 7.40961e6i) q^{97} -5.45131e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{2} - 64 q^{4} - 120 q^{5} - 377 q^{7} + 1024 q^{8} + 1920 q^{10} - 600 q^{11} - 5369 q^{13} - 3016 q^{14} - 4096 q^{16} + 24336 q^{17} + 32422 q^{19} - 7680 q^{20} - 4800 q^{22} - 106392 q^{23}+ \cdots - 10902624 q^{98}+O(q^{100}) \) 2 * q - 8 * q^2 - 64 * q^4 - 120 * q^5 - 377 * q^7 + 1024 * q^8 + 1920 * q^10 - 600 * q^11 - 5369 * q^13 - 3016 * q^14 - 4096 * q^16 + 24336 * q^17 + 32422 * q^19 - 7680 * q^20 - 4800 * q^22 - 106392 * q^23 + 63725 * q^25 + 85904 * q^26 + 48256 * q^28 - 177216 * q^29 + 268060 * q^31 - 32768 * q^32 - 97344 * q^34 + 90480 * q^35 + 229918 * q^37 - 129688 * q^38 - 61440 * q^40 + 112128 * q^41 + 115048 * q^43 + 76800 * q^44 + 1702272 * q^46 - 561336 * q^47 + 681414 * q^49 + 509800 * q^50 - 343616 * q^52 - 3575520 * q^53 + 144000 * q^55 - 193024 * q^56 - 1417728 * q^58 + 1786344 * q^59 + 1306837 * q^61 - 4288960 * q^62 + 524288 * q^64 - 644280 * q^65 + 2013817 * q^67 - 778752 * q^68 - 361920 * q^70 - 8121888 * q^71 - 7701278 * q^73 - 919672 * q^74 - 1037504 * q^76 - 226200 * q^77 - 1037231 * q^79 + 983040 * q^80 - 1794048 * q^82 - 9203568 * q^83 - 1460160 * q^85 + 920384 * q^86 - 307200 * q^88 - 2578608 * q^89 + 4048226 * q^91 - 6809088 * q^92 - 4490688 * q^94 - 1945320 * q^95 - 8555885 * q^97 - 10902624 * q^98

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